If `alpha` be a root of equation `x^2+x+1=0` then find the vlaue of `(alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2`

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

If alpha and beta are roots of the equation x^(2)-2x+1=0 , then the value of (alpha)/(beta)+(beta)/(alpha) is

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha is a positive root of the equation x^4 +x^3 -4x^2 +x+1=0 then alpha +1/alpha

If alpha and beta are roots of the equation px^(2)+qx+1=0 , then the value of alpha^(3)beta^(2)+alpha^(2)beta^(3) is

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If alpha,beta are the roots of the equation x^2-4x+1=0, then Find the value of: 1- alpha^2+beta^2 , 2- alpha^3+beta^3 , 3- |alpha-beta| , 4- 1/alpha+1/beta

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot